Fig. 2: Interacting flat band Hofstadter spectrum at CNP.

The spin degenerate interacting heavy fermion Hofstadter spectrum (b) contrasted with zero field strong coupling spectrum (a) in flat band (M = 0) limit at w₀/w₁ = 0.7 for both valleys at CNP. We fix \({m}_{\star} \) = \(\lceil \frac{q-3}{2}\rceil\). The B = 0 energies at Γ, labeled using \({{{{{{{{\mathcal{E}}}}}}}}}_{\pm }=\pm \frac{{U}_{1}}{4}+ \sqrt{\frac{{U}_{1}^{2}}{16}+{\gamma }^{2}}\), are recovered in B → 0 limit of our theory. The value of parameters used are J = 18.27 meV, U₁ = 51.72 meV, γ = − 39.11 meV, \({v}_{*}^{{\prime} }=1.624\,{{\mbox{eV}}}\,.\) Å, \({v}_{\ast} \) = −4.483 eV.Å and λ = 0.3792L_m. Following ref. ³⁶, twist angle θ = 1.05^∘ in this work and L_m = 134.218 Å. We set k_1,2 = 0, although inconsequential as magnetic subbands are Landau levels in this regime and thus do not disperse. The color labeling represents f-character of each energy eigenmode (see caption Fig. 1). The y-label E[meV] represents energy of subbands in meV.